Compact aero-thermo model stabilization with compressible flow function transform

ABSTRACT

Systems and methods for controlling a fluid based engineering system are disclosed. The systems and methods may include a model processor for generating a model output, the model processor including a set state module for setting dynamic states of the model processor, the dynamic states input to an open loop model based on the model operating mode, where the open loop model generates current state derivatives, solver state errors, and synthesized parameters as a function of the dynamic states and a model input vector, where a constraint on the current state derivatives and solver state errors is based a series of cycle synthesis modules. The series of cycle synthesis modules may include a flow module for mapping a flow curve relating a compressible flow function to a pressure ratio and for defining a solution point located on the flow curve and a base point located off the flow curve.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.14/769,860 filed Aug. 24, 2015, which is a US National Stage under 35USC § 371 of International Patent Application No. PCT/US2014/027601filed on Mar. 14, 2014, which claims priority to U.S. ProvisionalApplication No. 61/800,440 filed Mar. 15, 2013, the disclosures of whichare incorporated by reference herein in its entirety.

TECHNICAL FIELD OF THE DISCLOSURE

The present disclosure relates to the design and control of engineeringsystems, and more particularly, to design and control of fluid-basedengineering systems.

BACKGROUND

Fluid-based engineering systems are widely used and may include gasturbine engines for aviation and power generation, HVAC&R (heating,ventilation, air-conditioning and refrigeration), fuel cells, and other,more generalized fluid processing systems for hydrocarbon extraction,materials processing, and manufacture. These systems may contain any orall of the following components: turbo-machinery, fuel cell stacks,electric motors, pipes, ducts, valves, mixers, nozzles, heat exchangers,gears, chemical apparatuses and other devices for generating ormodifying a fluid flow.

Each of these applications places different operational demands on theengineering control system. In gas turbine engine applications, forexample, the relevant cycle is typically a Brayton turbine or firstEricsson cycle, and the basic thermodynamic parameters (or processvariables) are the pressure, temperature and flow rate of the workingfluid at the inlet, compressor, combustor, turbine, and exhaust. Theparameters may be related to the overall thrust, rotational energy, orother measure of power output. In order to precisely control this outputwhile maintaining safe, reliable and efficient engine operation, theengineering control system must be fast, accurate, robust, and providereal-time control capability across all required performance levels.While the relevant process variables vary depending on the system typeand configuration, the need for precise, efficient and reliableengineering control remains the same, as do the economic constraints onoverall cost and operational/maintenance requirements.

Further, because direct measurements of system parameters controlled maynot be possible (due to undeveloped technology, prohibitive cost,unreliable equipment, etc.), the control system may require real timeestimation of system parameters. System parameters may be mathematicalabstractions of engineering systems and/or process for a given set ofmeasured inputs used as control feedback.

In the past, control systems for such fluid-based engineering systemsrelied on piecewise linear state variable representations. These controlsystems, by their nature, were limited to relatively simple non-linearsystems. Another approach used in the past relies on semi-empiricalrelationships that tie important system parameters to control sensors;the drawback of such a system is that it may lack accuracy and isexpensive due to the additional hardware required for implementation.Other attempts have been made to deploy stationary simulations in aretail environment; however, by their nature, these models are large,use iterative solvers, have high maintenance cost and lack robustnesscritical in a real time environment.

A known approach to modern fluid-based engineering system control is theuse of component level physics based non-iterative mathematicalabstractions of fluid-based engineering systems. These mathematicalabstractions are conceptualized in a software environment specific tothe applied fluid-based engineering system. Such example systems andmethods for engineering system control are further detailed in U.S.Patent Pub. No. 2011/0052370 (“Robust Flow Parameter Model forComponent-Level Dynamic Turbine System Control”), which is herebyincorporated by reference.

A need exists for an engine parameter on-board synthesis (EPOS) in thereal-time control system of a fluid based engineering system that mayovercome the computational inefficiencies of prior EPOS models.

BRIEF DESCRIPTION

In accordance with an aspect of the disclosure, a control system isdisclosed. The control system may include an actuator configured toposition a control device. The control device defines a flow paththrough an aperture, the aperture defining a pressure drop along theflow path, and a control surface. The actuator positions the controlsurface in order to regulate fluid flow through the aperture. The systemmay include a control law configured to direct the actuator as afunction of a model output. The control system may include a modelprocessor configured to generate the model output, the model processorincluding an input object for processing a model input vector andsetting a model operating mode, a set state module for setting dynamicstates of the model processor, the dynamic states input to an open loopmodel based on the model operating mode. The open loop model generatescurrent state derivatives, solver state errors, and synthesizedparameters as a function of the dynamic states and the model inputvector. A constraint on the current state derivatives and solver stateerrors is based a series of cycle synthesis modules, each member of theseries of cycle synthesis modules modeling a component of a cycle of thecontrol device and including a series of utilities, the utilities arebased on mathematical abstractions of physical laws that govern behaviorof the component. The series of cycle synthesis modules may include aflow module for mapping a flow curve relating a compressible flowfunction to a pressure ratio and for defining a solution point locatedon the flow curve and a base point located off the flow curve. The modelprocessor may further include an estimate state module configured todetermine an estimated state of the model based on at least one of aprior state, the current state derivatives, the solver state errors, andthe synthesized parameters and an output object for processing at leastthe synthesized parameters of the model to determine the model output.

In a refinement, the open loop model may generate at least the solverstate errors as a function of a slope solver state defined between thebase point and the solution point.

In a further refinement, the slope solver state may be estimated bymoving the solution point along the flow curve, such that the solverstate errors are minimized.

In a further refinement, the control law may direct the actuator toposition the control surface based on a feedback that is a function ofthe slope solver state, such that the compressible flow function definesthe fluid flow and the pressure ratio defines the pressure drop.

In a further refinement, the control law may direct the actuator toposition the control surface under a condition of low fluid flow, suchthat a slope of the flow curve approaches zero at the solution point.

In another further refinement, the control law may direct the actuatorto position the control surface under a condition of choked fluid flow,such that an inverse slope of the flow curve approaches zero at thesolution point.

In another refinement, the model input vector may include one or more ofraw effector data, boundary conditions, engine sensing data, unitconversion information, range limiting information, rate limitinginformation, dynamic compensation determinations, and synthesizedlacking inputs.

In another refinement, the control device may be a gas turbine engine.

In a further refinement, the aperture may be a variable-area nozzle.

In accordance with another aspect of the disclosure, a method forcontrolling a control device is disclosed, the control device defining aflow path through an aperture, the aperture defining a pressure dropalong the flow path. The method may include generating a model outputusing a model processor. The control system may include generating themodel output, processing a model input vector and setting a modeloperating mode, and setting dynamic states of the model processor, thedynamic states input to an open loop model based on the model operatingmode. Current state derivatives, solver state errors, and synthesizedparameters may be generated as a function of the dynamic states and themodel input vector, where a constraint on the current state derivativesand solver state errors is based a series of cycle synthesis modules,each member of the series of cycle synthesis modules modeling acomponent of a cycle of the control device and including a series ofutilities, the utilities are based on mathematical abstractions ofphysical laws that govern behavior of the component. The series of cyclesynthesis modules may include a flow module for mapping a flow curverelating a compressible flow function to a pressure ratio and fordefining a solution point located on the flow curve and a base pointlocated off the flow curve. An estimated state of the model may bedetermined based on at least one of a prior state, the current statederivatives, the solver state errors, and the synthesized parameters.The method can also include processing at least the synthesizedparameters of the model to determine the model output. The method mayfurther include directing an actuator associated with the control deviceas a function of a model output using a control law and positioning acontrol device including a control surface using the actuator, where theactuator positions the control surface in order to regulate fluid flowthrough the aperture.

In a refinement, the open loop model may generate at least the solverstate errors as a function of at least a slope solver state definedbetween the base point and the solution point.

In a further refinement, the slope solver state may be estimated bymoving the solution point along the flow curve, such that the solverstate errors are minimized.

In a further refinement, the control law may direct the actuator toposition the control surface based on a feedback that is a function ofthe slope solver state, such that the compressible flow function definesthe fluid flow and the pressure ratio defines the pressure drop.

In a further refinement, the control law may direct the actuator toposition the control surface under a condition of low fluid flow, suchthat a slope of the flow curve approaches zero at the solution point.

In another further refinement, the control law may direct the actuatorto position the control element under a condition of choked fluid flow,such that an inverse slope of the flow curve approaches zero at theoperating point.

In accordance with another aspect of the disclosure, a gas turbineengine is disclosed. The gas turbine engine may include a fan, acompressor section downstream of the fan, and a combustor sectiondownstream of the compressor section, and a turbine section downstreamof the compressor section. Further, the gas turbine engine may includean actuator configured to position a control surface of an element ofthe gas turbine engine, the element of the gas turbine engine defining aflow path through an aperture, the aperture defining a pressure dropalong the flow path to regulate fluid flow through the aperture. The gasturbine engine may include a control law configured to direct theactuator as a function of a model output. The gas turbine engine mayinclude a model processor configured to generate the model output, themodel processor including an input object for processing a model inputvector and setting a model operating mode, a set state module forsetting dynamic states of the model processor, the dynamic states inputto an open loop model based on the model operating mode. The open loopmodel generates a current state derivatives, solver state errors, andsynthesized parameters as a function of the dynamic states and the modelinput vector, where a constraint on the current state derivatives andsolver state errors is based a series of cycle synthesis modules, eachmember of the series of cycle synthesis modules modeling a component ofa cycle of the gas turbine engine and including a series of utilities,the utilities are based on mathematical abstractions of physical lawsthat govern behavior of the component. The series of cycle synthesismodules may include a flow module for mapping a flow curve relating acompressible flow function to a pressure ratio and for defining asolution point located on the flow curve and a base point located offthe flow curve. The model processor may further include an estimatestate module for determining an estimated state of the model based on atleast one of a prior state, the current state derivatives, the solverstate errors, and the synthesized parameters and an output object forprocessing at least the synthesized parameters of the model to determinethe model output.

In a refinement, the aperture may include a variable-area nozzle.

In a refinement, the open loop model may generate at least the solverstate errors as a function of a slope solver state defined between thebase point and the solution point.

In a further refinement, the slope solver state may be estimated bymoving the solution point along the flow curve, such that the solverstate errors are minimized.

In a further refinement, the control law may direct the actuator toposition the control surface based on a feedback that is a function ofthe slope solver state, such that the compressible flow function definesthe fluid flow and the pressure ratio defines the pressure drop.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an exemplary control system for afluid-based engineering system.

FIG. 2 is a block diagram of an exemplary engine parameter on-boardsynthesis (EPOS) module of the control system of FIG. 1.

FIG. 3 is a block diagram of an exemplary CAM input object of the EPOSof FIG. 2.

FIG. 4 is a block diagram of an exemplary compact aero-thermal (CAM)object of the EPOS of FIG. 2.

FIG. 5 is a block diagram of an exemplary open-loop model of the CAMobject of FIG. 4.

FIG. 6 is a block diagram of an exemplary output conditioning module ofthe EPOS of FIG. 2.

FIG. 7A is a plot of pressure ratio versus compressible flow function,showing the relationship between a base point and the correspondingsolution state for a representative flow area.

FIG. 7B is a plot of pressure ratio versus compressible flow function,showing the choking areas and low pressure areas of the plot.

FIG. 8A is a plot of fLine versus normalized pressure ratio, showing twooptimization curves in accordance with the present disclosure.

FIG. 8B is a plot of fLine versus normalized compressible flow function,showing two optimization curves in accordance with the presentdisclosure.

FIG. 9 is a flowchart representative of machine readable instructionsthat may be executed to implement the example EPOS of FIGS. 1 and/or 2.

FIG. 10 is a flowchart representative of machine readable instructionsthat may be executed to implement the example CAM object of FIGS. 2and/or 4.

FIG. 11 is a block diagram of an example processing system that mayexecute the example machine readable instructions of FIGS. 9-10 and/orany elements of the present disclosure herein.

It should be understood that the drawings are not necessarily to scale.In certain instances, details which are not necessary for anunderstanding of this disclosure or which render other details difficultto perceive may have been omitted. It should be understood, of course,that this disclosure is not limited to the particular embodimentsillustrated herein.

DETAILED DESCRIPTION

Referring to the drawings and with specific reference to FIG. 1, acontrol system for a fluid-based engineering system in accordance withthe present disclosure is generally referred to by reference numeral100. Control demands may be generated by an operator interface 140 andmay be received by the engine parameter on board synthesis (EPOS) 110.For example, the operator interface 140 may be a real-time interfacesuch as a cockpit navigation system and/or an operator workstation.Additionally or alternatively, the operator interface 140 may includeanother, more generalized process control interface, which is suitablefor logging control commands to software control components 150,including, for example, a guidance, navigation, and control computer orautopilot system(s). Further, control demands may be generated by aninternal memory or any other internal programming operatively associatedwith software control elements 150.

The control elements 150 may include EPOS 110 and a control law 111 thatmay generate and/or process control instructions for the apparatus 130.The EPOS 110 and control law 111 may be implemented as software modulesdesigned to monitor, control, or otherwise act in associative functionwith regards to an apparatus 130. The control law 111 may obtain controlfeedbacks from the EPOS 110 and control commands from the operatorinterface 140. The control law 111 may generate control requests inengineering units to be processed by hardware control elements 120 tocontrol the apparatus 130.

Additionally, the software control components 150 may include an outputconditioner 113 and/or an input conditioner 115 to process output and/orinput data for the data's respective input/output destination. The inputto the EPOS 110, provided by the input conditioner 115, may be processedby fault detection and accommodation (FDA) logic 117 to detect rangefaults as well as in-range failures (e.g., rate-limit, cross-channelmismatch, etc.) and provide a reasonable input value along with a healthstatus indication for the input.

Further, the hardware control components 120 may convert digital datagenerated by the software control components 150 to an analog formreadable by the apparatus 130 (e.g., electrical signals), convert analogdata generated by the apparatus 130 into digital data readable softwarecomponents 150, condition such input and output data for readability,and/or control actuators 124 associated with the apparatus 130. Thedigital-to-analog convertor 122 can transform digital signals generatedby the control law 111 into actuator requests. The actuators 124 may beone or more devices which use control hardware to position variouscontrol components of the apparatus 130 in accordance with instructionsgenerated by the EPOS 110. Actuators, such as the actuators 124, may bedesigned to provide quick and accurate control of an apparatus.

Actuator sensors 125 may be included to measure various states of theactuators 124, wherein the actuator states (or positions) may be relatedto the physical configuration of the various control components of theapparatus 130. For example, fluid-based systems often include actuatorswhose linear or angular positions are sensed by actuator sensors 124,and which are related to the physical position of control surfaces orother control devices located proximate to a compressor, combustor,turbine and/or nozzle/exhaust assembly.

Further, the hardware control components 120 may include apparatussystem sensors 126. The apparatus system sensors 126 may measureoperational parameters associated with the apparatus 130. For example,fluid-based systems may include apparatus system sensors 126 thatmeasure the working fluid pressure, temperature and fluid flow atvarious axial and radial locations in the flow path. Apparatus systemsensors 126 may comprise a variety of different sensing devices,including, but not limited to, temperature sensors, flow sensors,vibration sensors, debris sensors, current sensors, voltage sensors,level sensors, altitude sensors and/or blade tip sensors. Apparatussystem sensors 126 may be positioned to measure operational parametersrelated to the function of apparatus 130, e.g., parameters related tocontrol commands submitted to EPOS 110 and control requests generated byEPOS 110 in order to direct actuators 124 to control apparatus 130.

Both the apparatus system sensors 126 and the actuator sensors 125 mayproduce electrical signals based upon a read-out result from saidsensors. The electrical signals produced by the actuator sensors 125 andthe apparatus system sensors 126 may be transmitted to ananalog-to-digital convertor 123. The analog-to-digital convertor mayconvert the electrical signals into digital signal data which may becompatible with and read by the EPOS 110 after processing by the inputconditioning module 115.

The apparatus 130 may be any fluid-based engineering system. Examplefluid-based engineering systems may include gas turbine engines foraviation and power generation, HVAC&R (heating, ventilation,air-conditioning and refrigeration), fuel cells, and other, moregeneralized fluid processing systems for hydrocarbon extraction,materials processing, and manufacture. In various embodiments, thephysical components of apparatus 130 include, but are not limited toincluding, compressors, combustors, turbines, shafts, spools, fans,blowers, heat exchangers, burners, fuel cells, electric motors andgenerators, reactor vessels, storage vessels, fluid separators, pipes,ducts, valves, mixers and other fluid processing or flow controldevices.

In some examples, the apparatus 130 may perform a thermodynamic cycle ona working fluid in order to generate rotational energy, electrical poweror reactive trust, to provide heating, ventilation, air conditioning andrefrigeration, or to perform other fluid processing functions. The rangeof available cycles includes, but is not limited to, the followingcycles and their derivatives: Otto cycles, Diesel cycles, Braytonturbine (or first Ericsson) cycles, Brayton jet (Barber/Joule) cycles,Bell-Coleman (reverse Brayton) cycles, Ericsson (Second Ericsson)cycles, Lenoir (pulse-jet) cycles, and Carnot, Stoddard and Stirlingcycles. Additionally or alternatively, apparatus 130 may perform anumber of individual thermodynamic processes for heating, cooling, flowcontrol, or for processing applications in agriculture, transportation,food and beverage production, pharmaceutical production, ormanufacturing, or for the extraction, transportation or processing of ahydrocarbon fuel. The range of available thermodynamic processesincludes, but is not limited to, adiabatic, isothermal, isobaric,isentropic, and isometric (isochoric or isovolumetric) transformations,exothermic reactions, endothermic reactions and phase changes.

In the present example, the apparatus 130 is a gas turbine engine. Assuch, the monitored aspects of the apparatus 130 may include, but arenot limited to, a compressor, combustor, turbine and/or nozzle/exhaustassembly. In an application for a gas turbine engine, the input andoutput values received/generated by the EPOS 110 may be vectorsrepresenting values for positions (i.e., nozzle areas, variable vaneangles, flow path areas, etc.), states, and actual sensed values ofparameters (i.e., spool speeds, gas path temperatures, pressuresproximate to components, flow rates proximate to components, etc.)related to the components of a gas turbine engine (i.e., a compressor,combustor, turbine and/or nozzle/exhaust assembly, etc.).

The data processed by the EPOS 110 are vectors containing parametersrelated to functions of the apparatus 130. Example input vectors for theEPOS 110 may include an external inputs vector (U_(E)) and a correctortruth vector (Y_(Ct)). U_(E) may contain values for external inputs tobe processed by the EPOS 110. U_(E) may describe the configurations,positions and states of various control elements in the apparatus 130.In a gas turbine engine, for example, individual elements of externalinputs vector U_(E) may have a set of values related to effectorposition; these effector position values may describe fuel flow rates,nozzle areas, variable vane angles, flow path orifice areas, and othercontrol element parameters. Further, U_(E) may have a set of valuesrelated to boundary conditions related to the operation of apparatus130. Some boundary conditions may be directly measured by apparatussystem sensors 126, such as fluid temperatures, pressures and flow ratesat physical boundaries of apparatus 130. In fluid-based applications,the boundary conditions may include boundary flow conditions and inletand outlet locations. Other boundary conditions specific to aircraftapplications include, but are not limited to, flight velocity, altitude,and bleed or power extractions parameters.

The corrector truth vector Y_(Ct) may contain data associated with realtime execution of the control system and describe the actual (sensed)values of the parameters related to the operation of apparatus 130. Theelements of Y_(Ct) may be based on measurements taken by the actuatorsensors 125 and/or the apparatus system sensors 126. Further, elementsof Y_(Ct) may be based on values derived from a well-understood andtrusted model of sensed parameters; for example, a flow rate model basedon a differential pressure drop across a Pitot tube or Venturi tube. Forgas turbine engines, typical Y_(Ct) vector elements include, but are notlimited to, spool speeds, gas path temperatures, and/or pressures allvalues of which may be proximate to engine components such ascompressors, combustors, and turbines. In the context of non-real timeapplications, including calibration, Y_(Ct) may correspond to highfidelity data which can either be physically tested or model-based.

Employing the compact aero-thermal model (CAM) of the presentdisclosure, FIG. 2 illustrates an embodiment of the EPOS 110 of FIG. 1in further detail. The EPOS 110 of FIG. 2 may include, but is notlimited to including a CAM input object 220, a compact aero-thermalmodel (CAM) object 230, and a CAM output object 240. The EPOS 110 mayreceive raw input data related to vectors U_(ERaw) and Y_(CtRaw).U_(ERaw) may contain values obtained from the actuator sensors 125, theapparatus system sensors 126 and/or any other associated sensors and/orinputs. Y_(CtRaw) may contain values obtained from the actuator sensors125, the apparatus system sensors 126 and/or any other associatedsensors and/or inputs.

The CAM input object 220 may package selected values from the receivedinput U_(E) vector into an input vector U_(E) _(_) _(in). Similarly, theCAM input object 220 may package selected values from the received inputinto an input corrector truth vector, Y_(Ct) _(_) _(in). Further, thevectors U_(E) _(_) _(in) and Y_(Ct) _(_) _(in) may then be conditionedto protect the input values; this may be done by range limiting thevalues, by constraining the values based on instructions, and/or byperforming any additional input modifications function on the vectors.The CAM input object 220 may also use the input vectors received todetermine an operating mode (OpMode) for the FADEC 110. The inputconditioning module 220 may output a conditioned external input vectorU_(E), a conditioned truth vector Y_(Ct), and an OpMode vector.

The input validity of the vector values may be ensured by faultdetection and accommodation logic (e.g., through processing from the FDAlogic 117) specific to each sensor input of the CAM input object 220.The fault detection and accommodation logic detects range faults as wellas in-range failures (i.e., rate-limit, cross-channel mismatch, etc.)and provides a reasonable value in all cases along with a health statusindication. An example CAM input object 220 is described in greaterdetail below with reference to FIG. 3.

The output of CAM input object 220 is received by the CAM object 230.The CAM object 230 may contain aero-thermal representations, orcomponent modules, of engine components. The component modules withinthe CAM object 230 may operate according to the system's constraintsrelated to mathematical abstractions of physical laws that governbehavior of the apparatus 130 (i.e., laws of conservation of energy,conservation of mass, conservation of momentum, Newton's 2^(nd) law forrotating systems, and/or any additional known calculable physics model).The system constraints for each contained module within the CAM object230 may have specific constraints programmed within to simulate amonitored area and/or function of the apparatus 130 (i.e., a bypass ductbleeds module, a low spool compressor module, a burner module, aparasitic power extraction module, etc.).

The CAM object 230 may use the input vectors along with internal solverstates, representing on-board corrector states, solver states, andphysics states, while functioning. The solver states may be introducedto address fast dynamics, resolve algebraic loops and smooth highlynon-linear model elements. The CAM object 230 may output a synthesizedparameters vector Y. The vector Y may be estimated in relation to theoperating range determined by the CAM object 230. An example CAM object230 is described in greater detail below with reference to FIG. 4.

The output of the CAM object 230 may be received by the CAM outputobject 240. The CAM output object 240 may post-process select CAMoutputs that are needed by consuming control software and/or hardware.For some outputs, the CAM output object 240 may perform a unitconversion, may apply a test adder, and/or may perform interpolationbetween ambient conditions and/or CAM output during starting operation.The CAM output object 240 may unpack the Y vector into values specificvalues desired by related components (i.e., temperatures, pressures,flows, sensor temperatures, and/or other output synthesis). The CAMoutput object 240 may also output inter-component station flows,temperatures, pressures, and/or fuel to air ratios, torque, thrust,bleed flows, and/or compressor and turbine case clearances. The CAMoutput object 240 may also indicate the current status (e.g., theaforementioned “OpMode” operating mode) as determined by the EPOS 110.An example CAM output object 240 is described in greater detail belowwith reference to FIG. 10.

Returning to the CAM input object 220, FIG. 3 illustrates an exemplaryembodiment of the CAM input object 220 of FIG. 2. The CAM input objectof FIG. 3 may include a U_(E) vector packager 310, a Y_(Ct) vectorpackager 320, an OpMode Determiner 330, and an input protection module340. The U_(E) vector packager may receive vector U_(ERaw) and the U_(E)vector packager 310 may select the desired values from the input vectorsand may create vector U_(E) _(_) _(in), which may be output to the inputprotection module 340. The U_(E) vector packager 310 may also be usedfor unit conversion and for synthesizing values for U_(E) which may notbe present. Similarly, the Y_(Ct) vector packager may receive vectorY_(CtRaw). The Y_(Ct) vector packager 310 may select the desired valuesfrom the input vectors and may create vector Y_(Ct) _(_) _(in), whichmay be output to the input protection module 340.

The OpMode determiner 330 may establish the operating mode of the CAMobject 230 based on the health status of input values that are necessaryto run in each operating mode. The health status may include status ofcontrol sensors determined by the FDA logic 117, as well as internallygenerated information by the CAM object 230, such as conditions ofinternal states and outputs. The OpMode determiner 330 may operate usinga logic design that seeks the highest fidelity mode based on availableinputs and may fall back to decreased fidelity modes to accommodatefaults. The operating mode determined by the OpMode determiner 330 isone of a programmed list of operating modes related to the function ofthe apparatus 130 and based on the input vector values and/or thecondition of CAM states and/or outputs. The functions of variousdownstream elements may be affected by the resulting operating modedetermined by the OpMode determiner 330.

Once the OpMode of the CAM is determined, the input protection module340 uses the OpMode vector and the input from the vector packagers 310,320 to determine input vectors U_(E) and Y_(Ct). Said vectors arereceived by the CAM object 230, illustrated in greater detail in FIG. 4.

The CAM object 230 may generate state vectors X_(C), X_(S), and X_(P).The physics state vector (X_(P)) contains simulated parameters relatedto dynamics of the apparatus 130 during a time of interested, whosederivatives (X_(pDot)) are calculated in an open loop model 410. Thevector X_(P) may include, but is not limited to including, spool shaftspeeds, apparatus material temperatures, etc. The solver state vectorX_(S) may contain values related to adjustments that are made to certaincomponents of the apparatus 130. These values may be adjustments to makeup for errors coming from the CAM. The X_(C) vector may contain valuesrelated to on-board corrector states, which are simulated componentlevel values that are a refinement of the Y_(Ct) vector to make themodeled Y_(C) vector comparable to the real values of Y_(Ct). Further,because the CAM object 230 may be implemented as a discrete real timesimulation, the CAM object 230 may fully execute each dynamic pass ofthe simulation, each pass being denoted by letter k. The product of eachsimulation pass k and simulation time step dt is the simulation time.The values of k may increase sequentially by 1, (e.g. k=[1, 2, 3, . . .]).

The set state module 420 may receive input of the U_(E), Y_(Ct), andOpMode vectors. Additionally, the set state module 420 may receive theprior state's values of the X vectors generated by the estimate statemodule 440. In FIG. 4, the prior state is denoted by the state “(k−1).”The set state module 420 may override the states in the X vectors with abase point value; however, if the values do not need an override, theset state module 420 may act as a pass through element. The overridefunctions of the set state module 420 may override the values within theX vectors with base-point (U) or external (Y_(Ct)) values depending onthe operating mode (OpMode) input to the CAM Module 230. To obtainoverride values, the set state module 420 may look up base-point valuesfor CAM states for use during initialization. The set state module 420may also select an active subset of solver states. As output, the setstate module 420 may generate corrector state (X_(C)), solver state(X_(S)), and physics state (X_(P)) vectors for use in the open loopmodel 410.

The open loop model 410 may consist of one or more cycle synthesismodules, each cycle synthesis module relating to a component, function,and/or condition associated with the apparatus 130. In the presentexample, the open loop model 410 is composed of a variety of cyclesynthesis modules that may represent components, functions and/orconditions associated with a cycle of apparatus 130. The open loopmodule is not limited to any specific number of modules and may containany number of modules that are used to simulate components, functions,and/or conditions associated with apparatus 130. The open loop model 410may receive input of the corrector state (X_(C)), solver state (X_(S)),and physics state (X_(P)) vectors from the set state module 420 and theeffector/boundary condition vector (U_(E)). The values input to the openloop model 410 may be used as input to the various modules simulatingthe components of apparatus 130. The open loop model 410 uses the valuesgenerated by the cycle synthesis modules to form a synthesizedparameters vector Y(k) based on U_(E)(k) and X(k). The synthesizedparameters vector Y(k) contains synthesized cycle values determined fromthe simulated physics of the open loop module 410 and may be used forcontrol of the apparatus 130.

Showing the series of cycle synthesis modules, FIG. 5 illustrates anexample embodiment of open loop model 410 of FIG. 4. The open loop model410 may include a group of primary stream modules 510, a group ofsecondary stream modules 520, a group of additional modules 530 and avector data packager 540. The open loop model 410 may receive input ofthe corrector state (X_(C)), solver state (X_(S)), and physics state(X_(P)) vectors, from the set state module 420, and the effector vector(U_(E)). The group of primary stream modules 510, the group of secondarystream modules 520, and the additional modules 530 all may receive inputfrom the corrector state (X_(C)), solver state (X_(S)), and physicsstate (X_(P)) vectors from the set state module 420 and the effectorvector (U_(E)). Further, the open loop module 410 is not limited toincluding the above mentioned groups of modules, but rather, the openloop module 410 may omit groups of modules and/or include other groupsof modules. Any and all modules of the open loop model 410 may interactwith one another to produce the output of each module.

Each module of the open loop module 410 may represent a component of theapparatus 130 and may be implemented by a library of utilities, whereineach utility may be a mathematical representation of the physicalproperties that make up various parts of component calculations. Forexample, utilities of the modules may include representations ofcompressors, turbines, bleeds, pressure losses, etc. that may bereusable throughout the CAM object 230 and may improve readability andmaintainability of the EPOS 110. These components may be built fromphysics representations of aerodynamic and thermodynamic processes. Eachmodule may produce, for example, an output vector containing, forexample, total pressure, total temperature, fuel/air ratio, and gas flowat the exit of the component, and/or any other parameter associated withthe modeled portion of the apparatus 130.

In some examples, the primary stream modules 510 may include, but arenot limited to including, the following based on corresponding elementsof the apparatus 130: a CMP_L module 605 modeling a low spoolcompressor, a D_BLD_STB 610 module modeling a bleed associated with alow spool compressor, a D_CS_INT module 615 modeling a pressure lossassociated with air flow passing through a duct of a compressor, a CMP_Hmodule 620 modeling a high spool compressor, a D_I030 625 modulemodeling a pressure loss associated with instrumentation in a duct atthe exit of a high spool compressor, a D_DIF_BURN module 630 modeling adiffuser, a BRN_PRI module 635 modeling a burner, a TRB_H module 640modeling a high spool turbine, a TRB_L module 645 modeling a low spoolturbine, a D_EGV_LT module 650 modeling a low turbine exit guide vaneduct, a D_I0495 module 655 modeling pressure losses associated withprobes aft of an exit guide vane duct, a D_I_NOZ_PRI module 660 modelingpressure losses related to air moving through a duct, the ductcontaining instrumentation probes, a D_TEC_NOZ module 665 modeling aprimary nozzle duct, a D_NOZ_PRI module 670 modeling pressure lossesassociated with the primary nozzle duct, and a NOZ_PRI module 675 aprimary nozzle. Additionally, the secondary stream modules 520 mayinclude, but are not limited to including, the following based oncorresponding elements of the apparatus 130: an example CMP_F_SEC module705 modeling a fan outer diameter compressor, a D_EGV_FO module 710modeling a fan exit guide vane duct, a D_BLD_SEC module 715 modeling anexit duct between a low compressor and a high compressor, a D_AVE_140module 720 modeling a duct downstream of a B25 bleed, a D_BLD_NOZ_SECmodule 725 modeling bypass duct bleeds of the apparatus 130, aD_I_NOZ_SEC module 730 modeling a secondary nozzle duct, and a NOZ_SECmodule 735 modeling a secondary nozzle. Further, there are severalmodules that are not associated with a particular stream, the modules530 may include, but are not limited to including, the following basedon conditions of the apparatus 130: a POWER_EXTRACT module 805 modelingeffects of energy and/or efficiency losses of the apparatus 130, aFAN_ID_POWER module 810 modeling an accounting for power loss from a fangear box of the apparatus 130, and a TORQUE_BALANCE module 815 modelingan accounting for conservation of energy related to unsteady torquebalance within the apparatus 130, and a CALC_ERR_SLVR module 820 thatforms solutions to errors detected in the OLM 410. Further, anyadditional modules and/or groups of modules modeling any additionalphysical properties associated with the apparatus 130 may be included aspart of the open loop model 410.

The example modules of FIG. 5 may be designed using one or morephysics-based configurable utilities. The configurable utilities may becontained in a library of subsystems within the EPOS structure. The openloop module 440 may compile the above mentioned modules from thesubsystems of physics-based configurable utilities based onpreprogrammed instructions and/or a user input.

Once data is processed throughout various modules of the open loop model410, the vector data packager 540 receives input data from the group ofprimary stream modules 510, the group of secondary stream modules 520,and the additional modules 530. In addition to the synthesizedparameters vector Y(k) based on the model state and input, the open loopmodel may also output a solver errors vector (ErrSlvr) related to thesolver states vector (X_(S)). Also, the open loop model 410 may collectand output a physics state derivatives vector (X_(PDot)). The receiveddata may be packaged by the vector data packager 540 in the form ofvectors Y(k), ErrSlvr, and X_(PDot). Further, the vector data packagermay package vector data into fewer vectors and/or additional vectors.

Certain utilities used to comprise said modules of the open loop model410 may model gas-based properties and may represent, for example,specific heat as a function of temperature and fuel/air ratio, relativepressure as a function of enthalpy and fuel/air ratio, enthalpy as afunction of temperature and fuel/air ratio, specific heat ratio as afunction of temperature and fuel/air ratio, relative pressure as afunction of temperature and fuel/air ratio, relative pressure as afunction of temperature and fuel/air ratio, temperature as a function ofenthalpy and fuel/air ratio, and/or gas constant and specific heat ratioas a function of temperature and fuel/air ratio. Other example utilitiesmay model thermal conductivity as a function of gas total temperature,the absolute viscosity as a function of gas total temperature, criticalflow parameters as a function of specific heat and a gas constant,coefficients of thermal expansion as a function of material temperatureand/or type, material specific heat as a function of materialtemperature and/or type, and/or material thermal conductivity as afunction of material temperature and type. Further, other utilitiesmodeling other gas related functions may be present. Additionally oralternatively, any other utilities modeling any other propertiesassociated with the apparatus 130 may be included.

Additionally, the modules comprising the open loop model 410 may includeone or more configurable utilities. The configurable utilities may becomplex representations of engine components. For example, aconfigurable utility may represent a particular physical effect in majorengine components such as a compressor or a turbine. Each instance of aconfigurable utility may be selected to be one of severalrepresentations of the physical processes it models, even though theinterface of the configurable model remains unchanged. Configurableutilities may reconfigure themselves to represent a particular componentby switching the underlying configurable subsystems. Using suchconfigurable utilities may benefit the maintainability of a softwareapplication of the open loop model 430.

In an example embodiment, a configurable utility may be designed tomodel a Reynolds effect in the compressors of the apparatus 130 and mayreconfigure itself to represent a particular component of the compressor(e.g., a high spool compressor, a low spool compressor, etc.). Thisexample configurable, compressor Reynolds effect utility may be used information of cycle synthesis modules and may be used in modulessimulating a low spool compressor (e.g., the CMP_L module 605 of FIG.5), a high spool compressor (e.g., the CMP_H module 620 of FIG. 5),and/or any other module associated with a compressor simulation.Similarly, specific modules of the open loop model 410 may utilize aconfigurable utility to model Reynolds effect in the turbines of theapparatus 130 and may reconfigure itself to represent a particularcomponent of the compressor.

In an example OLM 410, a specific utility may model physical processesof a compressor of the apparatus 130 and may include representations ofsuch physical processes as sub-utilities. Sub-utilities of an examplecompressor utility may include, but is not limited to including, basicphysics utilities associated with the basic physics of the apparatus 130(e.g., isentropic compression, laws of thermodynamics, ideal gasproperties, etc.), a component aero-thermal map evaluation, gas-materialheat transfer properties, models of component bleeds, torque componentsfrom adiabatic steady-state, and/or effects of scaling between map andcycle conditions (design, gas property, Reynolds effect, clearance,untwisting effects, etc.). The output of such a compressor utility mayinclude, but is not limited to including, component exit gas flowconditions, bleed flows, swirl angles, total component inlet gas flows,torque extracted, and derivatives of material temperatures. A compressorutility may be operatively associated with other utilities (e.g.,off-board correction look up tables with selectable schedulingparameters, a selector for enabling on-board and/or off-board correctionfor the component, etc.) to form a compressor-related module like, forexample, the CMP_L module 605 and/or the CMP_H module 620.

Another example of an OLM model utility is the turbine utility.Sub-utilities of an example turbine utility may include, but are notlimited to including, basic physics utilities associated with the basicphysics of the apparatus 130 (e.g., isentropic expansion, laws ofthermodynamics, ideal gas properties, etc.), a component aero-thermalmap evaluation, gas-material heat transfer properties, models of inletguide vanes, models of consolidated turbine cooling bleeds, rotor inlettemperature calculation, turbine clearance effects, and/or effects ofscaling between map and cycle conditions (design, gas property, Reynoldseffect, clearance, untwisting effects, etc.). Outputs of such an exampleturbine utilities may include, but are not limited to including,component exit gas conditions, rotor inlet temperature, flows into theturbine, generated torque, material temperature derivatives, steadystate material temperature at current conditions, material temperaturetime constants, radius of apparatus from thermal expansion, and/orclearance values. A turbine utility may be operatively associated withother utilities (e.g., off-board correction look-up tables withselectable scheduling parameters, a selector for enabling on-boardand/or off-board correction for the component, etc.) to form acompressor-related module like, for example, the TRB_H module 640 and/orthe TRB_L module 645.

Returning to FIG. 4, the sensing synthesis module 430 may model controlsensor measurements that differ from corresponding average gas pathengine station estimates packaged in Y due to regime/location effects inthe sensor surroundings and sensor body thermal inertia. Receiving inputof Y and the derivative physics state vector (X_(PDot)), the sensingsynthesis module 430 may act as another means of fault or errordetection within the CAM module 230.

Receiving input of Y(k), Y_(C)(k), X_(PDot)(k), and/or ErrSlvr(k), theestimate state module 440 may use said inputs to determine the next passvalue of CAM state vector X(k). The estimate state module 440 may scaleand correct solver state error vector, select solver gain schedulingparameters, calculate solver state gains, calculate scale, and correctthe corrector state error vector, integrate state derivatives, applystate integrator range limits, reset state integrators duringinitialization, detect saturated state integrators, and/or detectinternal errors indicated by unreasonably large synthesized values.

The estimate state module 440 may receive input of the effector vector(U_(E)), the synthesized parameters vector (Y), the on-board correctorstate vector (X_(C)), the physics state vector (X_(P)), the solver statevector (X_(S)), the solver errors vector (errSlver), and the physicsstate derivatives vector (X_(PDot)). The estimate state module 440 mayoutput updated versions of the on-board corrector state vector (X_(C)_(_) _(ESM)), the physics state vector (X_(P) _(_) _(ESM)), and thesolver state vector (X_(S) _(_) _(ESM)). These vectors are the analyzedstate vectors from the current iteration of the open loop model 410.

The output of the estimate state module 440 is received by the CAMoutput object 240, which is illustrated in FIG. 6. The CAM output object240 may include, but is not limited to including, a vector unpacker 910,a temperatures valuator 920, a pressures valuator 930, a flows valuator940, a sensor temperatures valuator 950, an other output synthesizer960, and a status indicator 970. The vector unpacker 910 may receiveinput of the synthesized parameters vector (Y). The vector unpacker 910may output the unpacked Y vector to other elements of the outputconditioning module. The status indicator 970 may receive input of theoperating mode vector (OpMode). Further, the output conditioning module240 is not limited to including the above mentioned elements, butrather, output conditioning module 240 may omit elements and/or includeother elements.

The temperatures valuator 920 may process temperature related values ofthe synthesized parameters vector (Y). This may include performing unitconversions, implementing test adders, performing non-linearinterpolation between temperature values during the starting functionsof the apparatus 130, and/or obtaining temperature values from defaulttables as backup if/when needed. The temperatures valuator 920 is notlimited to functioning in the above mentioned manner, rather, thetemperatures valuator 920 may omit any of the listed functions and/oradd additional functions related to processing temperature data of thesynthesized parameters vector (Y).

The pressures valuator 930 may process pressure related values of thesynthesized parameters vector (Y). This may include performing unitconversions, implementing test adders, performing non-linearinterpolation between pressure values during the starting functions ofthe apparatus 130, and/or obtaining pressure values from default tablesas backup if/when needed. The pressures valuator 930 is not limited tofunctioning in the above mentioned manner, rather, the pressuresvaluator 930 may omit any of the listed functions and/or add additionalfunctions related to processing pressure data of the synthesizedparameters vector (Y).

The flows valuator 940 may process fuel flow related values of thesynthesized parameters vector (Y). This may include performing unitconversions, implementing test adders, performing non-linearinterpolation between fuel flow values during the starting functions ofthe apparatus 130, and/or obtaining fuel flow values from default tablesas backup if/when needed. The flows valuator 940 is not limited tofunctioning in the above mentioned manner, rather, the flows valuator940 may omit any of the listed functions and/or add additional functionsrelated to processing fuel flow data of the synthesized parametersvector (Y).

The sensor temperatures valuator 950 may process sensor temperaturerelated values of the synthesized parameters vector (Y). This mayinclude performing unit conversions, implementing test adders,performing non-linear interpolation between temperature values duringthe starting functions of the apparatus 130, and/or obtaining sensortemperature values from default tables as backup if/when needed. Thesensor temperatures valuator 950 is not limited to functioning in theabove mentioned manner, rather, the sensor temperatures valuator 950 mayomit any of the listed functions and/or add additional functions relatedto processing sensor temperature data of the synthesized parametersvector (Y).

The other output synthesizer 960 may process other output data of thesynthesized parameters vector (Y) not processed by the temperaturesvaluator 920, the pressures valuator 930, the flows valuator 940, thesensors and/or the temperatures valuator 950. This may includeperforming unit conversions, implementing test adders, performingnon-linear interpolation between temperature values during the startingfunctions of the apparatus 130, and/or obtaining other output valuesfrom default tables as backup if/when needed. The flows valuator 940 isnot limited to functioning in the above mentioned manner, rather, theflows valuator 940 may omit any of the listed functions and/or addadditional functions related to processing other output data of thesynthesized parameters vector (Y).

The status indicator 970 may receive input from the operating modevector (OpMode). Using this input, the status indicator 970 may generateand provide a status indication of the operating status of the CAMmodule 230 for use in any downstream logic devices.

Many component level mathematical abstractions of components in theapparatus 130 reduce to a non-linear state space. As such, a controlhardware and model size may impose low limits on simulation time step,which in turn limits bandwidth of the system states that can beestimated while meeting fidelity and numerical stability margin targets.However, subsets of the state exceeding upper limits of bandwidth maynot impact the model fidelity on the time scale of interest.Optimization of the control system 100 may “slow” dynamics of the “fast”states while achieving stable and accurate simulation.

For systems with known local “strong” non-linearities, an “indirect”approach may be employed, wherein stabilizing dynamics are introducedlocally with a state estimation whose only purpose is to smooth thelocal non-linearity while preserving system space fidelity. An exampleof such local non-linearity is a compressible flow function. Acompressible flow function may be used in component level system modelsto represent flow through a nozzle/orifice and pressure loss in ducts.

Turning now to the plot diagrams of FIGS. 7A and 7B, mappings for acompressible flow function associated with a variable area flow at anelement of the apparatus 130 are shown. FIG. 7A illustrates therelationship between pressure ratio (PR) and the compressible flowfunction (CFF) for a variable area flow regulation device associatedwith the apparatus 130. Pressure ratio is defined as the ratio ofupstream to downstream pressure across a flow area A and is plotted onthe horizontal axis. Compressible flow function is a function of theflow through area A and is plotted on the vertical axis, resulting inthe shown curve in the form CFF=f(PR).

Such analysis originates from compressible flow theory as applied to acomponent-level mathematical model of the apparatus 130. In theparticular embodiment of FIG. 7A, for example, the CFF is defined asfollows:

${CFF} = {\frac{W}{P}\sqrt{T}}$where mass flow W, pressure P, and temperature T are defined for theflow area, for example upstream or downstream of the flow aperture. Someexamples may include bleed flow, in which compressed air flows from ahigher pressure region to a lower pressure region through a bleedorifice; nozzle flow, in which high pressure, high velocity combustiongas expands to static conditions in an ambient reservoir; and flowregulation, in which a variable area restriction is placed in the gasstream in order to generate a loss in pressure.

Depending on the component level architecture, the curves of FIGS. 7Aand 7B can be interpreted as a map of pressure ratio based on CFF(marker 50). In such interpretations, mapping may be concerned withchoking when small changes in the CFF result in large changes in thepressure ratio. Alternatively, the curve may be interpreted as a map ofCFF based on pressure ratio, where the mapping may be concerned with apressure ratio near a value of 1, wherein small changes in pressureratio result in large changes in CFF (marker 60). Flow curves approachthe region of choked flow and have “well behaved” modeling ranges. Therange is determined in the region above zero flow (i.e., where CFF=0),and below choked flow (e.g., below CFFmax), between minimum and maximumCFF as defined by PRmax. In the choked flow region above PRmax, theslope of the flow curve tends to diverge (that is, the inverse slopeapproaches zero), and relatively small changes in CFF correlate withrelatively large changes in pressure ratio. Similarly, in the low flowregion below PRmin, the slope of the flow curve approaches zero (thatis, the inverse slope diverges), and relatively small changes inpressure ratio PR correlate with relatively large changes in CFF.

Both situations can lead to instabilities and present substantialchallenges to the discrete solver approach to system control. In chokedflow conditions, pressure ratio cannot always be independentlydetermined from CFF. Such determinations regarding choked and unchokedstates may be made in the open loop model 410.

Returning to FIG. 7A, a plot of the CFF versus the pressure ratio isshown, illustrating the relationship between base point P1 and acorresponding solution state fLine. A particular value of solution stateA is shown graphically with fLine(i) as drawn between base point P1 andsolution point P2 on the flow curve A. The goal is to generate solutionpoint P2 as an operational modeling point with high fidelity; that is,such that CFF and pressure ratio correspond as closely as possible totheir actual (measured or analytically derived) values across theaperture area.

The methods of using CFF in the EPOS 110 may ensure robust flow andpressure ratio calculations across the operating range, including thelow-flow and choked flow regions. The fLine is defined with a slope ofthe line extending from a base point located off the curve and selectedto ensure robust mapping of pressure ratio PR and CFF across the entireoperating range, including both the low-flow region below PR(i) andthroughout the approach to choked flow above PRmax.

Further, fLine may be determined by the slope of the fLine(i) between P1and P2, where the solution point lies anywhere along curve A between thePRmax and 0. This generates a relationship between pressure ratio andCFF as a function of the solution state fLine, rather than the slope ofarea curve A. By selecting base point P1 appropriately, pressure ratioand CFF are reliably mapped in regions below PRmin and above PRmax.

Plots showing the functions for PR(fLine) and CFF(fLine) are illustratedin FIGS. 8A and 8B, respectively. In general, an aim of optimization forthe functions PR(fLine) and CFF(fLine) is to make the functions as“linear” as possible, thus reducing the variations of gain in thestabilizing system and enabling adequate estimation of stabilitymargins. The requirement of “quasilinearity” of CFF(fLine) and PR(fLine)can be formulated as constraints on curvatures of the graphs of thesefunctions, where for any curve (x(t), y(t)), the curvature is definedby:

$\kappa = {\frac{\left| {{x^{\prime}y^{''}} - {y^{\prime}x^{''}}} \right|}{\left( {x^{2} + y^{2}} \right)^{3\text{/}2}}.}$Note that these curvatures cannot be too small due to the identity:

$\frac{d\mspace{14mu}{CFF}}{d\mspace{14mu}{PR}} = {\frac{d\mspace{14mu}{CFF}}{d\mspace{14mu}{fLine}}\left( \frac{d\mspace{14mu}{PR}}{d\mspace{14mu}{fLine}} \right)^{- 1}}$which implies that the variations of the derivatives on the right sidecannot both be small.

Additionally, a transformation formula:fLine=(CFF−CFFb)/(PR−PRb)implies that the parameter PRb must not be close to the range of thevariable PR: otherwise, fLine peaks as PR gets closer to PRb, which maycontradict the purpose of transformation. This fact, and the boundnessof the derivatives, implies that fLine is quasi-linear with respect toCFF as long as the (dCFF/dPR) is not vanishing. Thus, the requirement onthe curvature of CFF(fLine) may not be needed. As long as the curvatureof PR(fLine) is bounded, the function CFF(fLine) consists of twointervals: the function is close to linear on the first and close tohorizontal on the second. Therefore, two criterions for optimization ofthe parameters CFFb and PRb are the curvature of the graph (fLine, PR)must be minimal and the horizontal interval of the graph of the functionCFF(fLine) must be minimal.

With respect to the above mentioned criterions for optimization, aconstraint C must be fixed that bounds the curvature of the graph(fLine, PR), and optimizes the minimal horizontal interval of theCFF(fLine) function. To avoid being trapped in local minima and tofacilitate numerical stability of optimization procedure, optimizationmay be performed with respect to artificially constructed variablesinstead of the parameter pair (CFF0, PR0):

${x_{1} = {\frac{d\left( {CFF}_{\min} \right)}{d({fLine})} = {{PR}_{\min} - {{PR}\; 0}}}},{x_{2} = {\left( \frac{d\left( {PR}_{\max} \right)}{d({fLine})} \right)^{- 1} = {- {\frac{{CFF}_{\max} - {{CFF}\; 0}}{\left( {{PR}_{\max} - {{PR}\; 0}} \right)^{2}}.}}}}$Other possible transformations may be used to smooth the CFF(fLine),such as constructing the fLine such that:

$\frac{d\mspace{14mu}{CFF}}{d\mspace{14mu}{fLine}} = {\left( \frac{d\mspace{14mu}{PR}}{d\mspace{14mu}{fLine}} \right)^{- 1} = \sqrt{\frac{d\mspace{14mu}{CFF}}{d\mspace{14mu}{PR}}}}$and a similar result may be achieved by choosing:fLine=(PR^(−3.3)−1).

fLine is an actively defined state in which the corresponding elementsof error processed by the estimate state module 440 are determined byappropriate functional relationships with the corresponding incrementalchanges to pressure ratio and CFF.

The CFF implemented fLine may be used to determine pressure loss in afriction loss application wherein the flow at the orifice is known.Additionally, CFF implemented fLine may be used to determine flow whenthe pressure ratio is known for orifice flow applications.

While an example manner of implementing the EPOS 110 of FIG. 1 has beenillustrated in FIGS. 2-6, one or more elements, processes, and/ordevices illustrated in FIGS. 2-6 may be combined, divided, rearranged,omitted, eliminated and/or implemented in any other way. Further, theexample elements of FIGS. 1-6 could be implemented by one or morecircuit(s), programmable processor(s), application specific integratedcircuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or fieldprogrammable logic device(s) (FPLD(s)), etc. When any of the apparatusor system claims of this patent are read to cover a purely softwareand/or firmware implementation, at least one of the example elements arehereby expressly defined to include a tangible computer readable mediumsuch as a memory, DVD, CD, Blu-ray, etc. storing the software and/orfirmware. Further still, the example embodiments of have beenillustrated in may include one or more elements, processes and/ordevices in addition to, or instead of, those illustrated in FIGS. 1-6,and/or may include more than one of any or all of the illustratedelements, processes and devices.

Flowcharts representative of example machine readable instructions areshown in FIGS. 9 and 10. In these examples, the machine readableinstructions comprise a program for execution by a processor such as theprocessor such as the processor 1210 shown in the example computer 1200discussed below in connection with FIG. 11. The program may be embodiedin software stored on a tangible computer readable medium such as aCD-ROM, a floppy disk, a hard drive, a digital versatile disk (DVD), aBlu-ray disk, or a memory associated with the processor 1210, but theentire program and/or parts thereof could alternatively be executed by adevice other than the processor 1210 and/or embodied in firmware ordedicated hardware. Further, although the example programs are describedwith reference to the flowcharts illustrated in FIGS. 9 and 10, manyother methods of implementing embodiments of the present disclosure mayalternatively be used. For example, the order of execution of the blocksmay be changed, and/or some of the blocks described may be changed,eliminated, or combined.

With reference to FIG. 9, example machine readable instructions 1000 maybe executed to implement the EPOS 110 of FIGS. 1 and/or 2. Withreference to FIGS. 1 and/or 2, the example machine readable instructions1000 begin execution at block 1010 at input vectors are received by theCAM input object 220 and are used by the CAM input object 220 todetermine the operating mode (OpMode) of the simulation and to compilethe CAM input vectors U_(E) and Y_(Ct) (block 1015). The CAM inputvectors are then used by the CAM object 230 to determine synthesizedparameters vector Y based on internal physics state module of the CAMmodule 230 and the external inputs U_(E), Y_(Ct), and OpMode (block1020). The synthesized parameters vector Y is conditioned by the CAMoutput object 240 for use by external modules such as, for example, thecontrol law 123 of FIG. 1 (block 1025).

The example machine readable instructions 1100 of FIG. 10 may beexecuted to implement the CAM object 230 of FIGS. 2 and/or 4. Withreference to FIGS. 2 and/or 4, the set state module receives input fromand sets the state of the CAM object 230 based upon vectors U_(E),Y_(C)(k), OpMode, and prior physics state vectors generated by theestimate state module 440 in the form of X_(E) _(_) _(ESM)(k−1), X_(C)_(_) _(ESM)(k−1), and X_(P) _(_) _(ESM)(k−1) (block 1110). The open loopmodel 410 determines synthesized parameters vector Y(k) by processingdata contained in U_(E), Y_(C)(k), X_(C)(k−1), X_(S)(k−1), andX_(P)(k−1) using one or more contained cycle synthesis modules, the oneor more cycle synthesis modules being a mathematical abstraction(s) ofthe physics states associated with an element of a cycle of theapparatus 130 (block 1115). The sensing synthesis module 430 receivesthe synthesized parameters vector Y(k) and detects potential errors inthe vector (block 1120). The estimate state module 440 determines thephysics state vectors X_(S) _(_) _(ESM)(k), X_(C) _(_) _(ESM)(k), andX_(P) _(_) _(ESM)(k) for the present state (k) (block 1125). Theestimate state module 440 outputs the vectors X_(S) _(_) _(ESM)(k),X_(C) _(_) _(ESM)(k), and X_(P) _(_) _(ESM)(k) to the set state module420 for processing the next sequential state (block 1130). The estimatestate module 440 outputs the vector Y(k) for use external to the CAMmodule 230 (block 1135).

FIG. 11 is a block diagram of an example computer 1200 capable ofexecuting the instructions of FIGS. 9-10 to implement the apparatus ofFIGS. 1-6. The computer 1200 can be, for example, a server, a personalcomputer, or any other type of computing device.

The system 1200 of the instant example includes a processor 1210. Forexample, the processor 1210 can be implemented by one or moremicroprocessors or controllers from any desired family or manufacturer.

The processor 1210 includes a local memory 1215 and is in communicationwith a main memory including a read only memory 1230 and a random accessmemory 1220 via a bus 1240. The random access memory 1220 may beimplemented by Synchronous Dynamic Random Access Memory (SDRAM), DynamicRandom Access Memory (DRAM), RAMBUS Dynamic Random Access Memory (RDRM)and/or any other type of random access memory device. The read onlymemory 1230 may be implemented by a hard drive, flash memory and/or anyother desired type of memory device.

The computer 1200 also includes an interface circuit 1250. The interfacecircuit 1250 may be implemented by any type of interface standard, suchas an Ethernet interface to network 1260, a universal serial bus (USB),and/or a PCI express interface.

One or more input devices 1254 are connected to the interface circuit1250. The input device(s) 1254 permit a user to enter data and commandsinto the processor 1210. The input device(s) can be implemented by, forexample, a keyboard, a mouse, a touchscreen, a track-pad, a trackball,isopoint and/or a voice recognition system. The interface 1250 mayoperate in conjunction with, in parallel with, or in place of, theoperator interface 115 of FIG. 1.

One or more output devices 1258 are also connected to the interfacecircuit 1250. The output devices 1258 can be implemented by, forexample, display devices for associated data (e.g., a liquid crystaldisplay, a cathode ray tube display (CRT), etc.), and/or an actuatoroperatively associated with a fluid-based engineering system such as gasturbine engines for aviation and power generation, HVAC&R (heating,ventilation, air-conditioning and refrigeration), fuel cells, and other,more generalized fluid processing systems for hydrocarbon extraction,materials processing, and manufacture.

From the foregoing, it can be seen that the technology disclosed hereinhas industrial applicability in a variety of settings such as, but notlimited to, systems and methods for controlling a fluid basedengineering system. Example fluid-based engineering systems may includegas turbine engines for aviation and power generation, HVAC&R (heating,ventilation, air-conditioning and refrigeration), fuel cells, and other,more generalized fluid processing systems for hydrocarbon extraction,materials processing, and manufacture. Using the teachings of thepresent disclosure, compact aero-thermal models of fluid-basedengineering systems may be designed to reduce computational load on asystem's control device and/or on board processor. The efficiency ofsuch a model may be improved through the use of a series of utilities,the utilities based on mathematical abstractions of physical propertiesassociated with components of the engineering system. This improvementover the prior art may conserve computational efficiency and may improvethe accuracy of the control system for fluid based engineering systems.

While the present disclosure has been in reference to a gas turbineengine of an aircraft, one skilled in the art will understand that theteachings herein can be used in other applications as well, as mentionedabove. It is therefore intended that the scope of the invention not belimited by the embodiments presented herein as the best mode forcarrying out the invention, but that the invention will include allequivalents falling within the spirit and scope of the claims as well.

What is claimed is:
 1. A control system, comprising: an actuatorconfigured to position a control device, the control device defining aflow path through an aperture, the aperture defining a pressure dropalong the flow path, and comprising a control surface, wherein theactuator positions the control surface in order to regulate fluid flowthrough the aperture; a control law configured to direct the actuator asa function of a model output; and a model processor configured togenerate the model output, the model processor comprising: an inputobject for processing a model input vector and setting a model operatingmode; a set state module for setting dynamic states of the modelprocessor, the dynamic states input to an open loop model based on themodel operating mode; wherein the open loop model generates currentstate derivatives, solver state errors, and synthesized parameters as afunction of the dynamic states and the model input vector, wherein aconstraint on the current state derivatives and solver state errors isbased on a series of cycle synthesis modules, each member of the seriesof cycle synthesis modules modeling a component of a cycle of thecontrol device and comprising a series of utilities, the utilities basedon mathematical abstractions of physical laws that govern behavior ofthe component, the series of cycle synthesis modules including a flowmodule for optimized mapping a flow curve relating a compressible flowfunction to a pressure ratio and for defining a solution point locatedon the flow curve and a base point located off the flow curve, whereinthe optimized mapping comprises minimization of curvature of the flowcurve related to the pressure ratio while minimizing a horizontalportion of the flow curve related to the compressible flow function; anestimate state module configured to determine an estimated state of themodel based on at least one of a prior state, the current statederivatives, the solver state errors, and the synthesized parameters;and an output object for processing at least the synthesized parametersof the model to determine the model output.
 2. The control system ofclaim 1, wherein the open loop model generates at least the solver stateerrors as a function of a slope solver state defined between the basepoint and the solution point.
 3. The control system of claim 2, whereinthe slope solver state is estimated by moving the solution point alongthe flow curve, such that the solver state errors are minimized.
 4. Thecontrol system of claim 3, wherein the control law directs the actuatorto position the control surface based on a feedback that is a functionof the slope solver state, such that the compressible flow functiondefines the fluid flow and the pressure ratio defines the pressure drop.5. The control system of claim 4, wherein the control law directs theactuator to position the control surface under a condition of low fluidflow, such that a slope of the flow curve approaches zero at thesolution point.
 6. The control system of claim 4, wherein the controllaw directs the actuator to position the control surface under acondition of choked fluid flow, such that an inverse slope of the flowcurve approaches zero at the solution point.
 7. The control system ofclaim 1, wherein the model input vector includes at least one of raweffector data, boundary conditions, engine sensing data, unit conversioninformation, range limiting information, rate limiting information,dynamic compensation determinations, and synthesized lacking inputs. 8.The control system of claim 1, wherein the control device is a gasturbine engine.
 9. The control system of claim 8, wherein the aperturecomprises a variable-area nozzle.
 10. A method for controlling a controldevice, the control device defining a flow path through an aperture, theaperture defining a pressure drop along the flow path, the methodcomprising: generating a model output using a model processor;processing a model input vector and setting a model operating mode;setting dynamic states of the model processor, the dynamic states inputto an open loop model based on the model operating mode; generatingcurrent state derivatives, solver state errors, and synthesizedparameters as a function of the dynamic states and the model inputvector, wherein a constraint on the current state derivatives and solverstate errors is based on a series of cycle synthesis modules, eachmember of the series of cycle synthesis modules modeling a component ofa cycle of the control device and comprising a series of utilities, theutilities based on mathematical abstractions of physical laws thatgovern behavior of the component, the series of cycle synthesis modulesincluding a flow module for optimized mapping a flow curve relating acompressible flow function to a pressure ratio and for defining asolution point located on the flow curve and a base point located offthe flow curve, wherein the optimized mapping comprises minimization ofcurvature of the flow curve related to the pressure ratio whileminimizing a horizontal portion of the flow curve related to thecompressible flow function; determining an estimated state of the modelbased on at least one of a prior state, the current state derivatives,the solver state errors, and the synthesized parameters; and processingat least the synthesized parameters of the model to determine the modeloutput; directing an actuator associated with the control device as afunction of the model output using a control law; and positioning thecontrol device comprising a control surface using the actuator, whereinthe actuator positions the control surface in order to regulate fluidflow through the aperture.
 11. The method of claim 10, wherein at leastthe solver state errors are generated as a function of at least a slopesolver state defined between the base point and the solution point. 12.The method of claim 11, wherein the slope solver state is estimated bymoving the solution point along the flow curve, such that the solverstate errors are minimized.
 13. The method of claim 12, wherein thecontrol law directs the actuator to position the control surface basedon a feedback that is a function of the slope solver state, such thatthe compressible flow function defines the fluid flow and the pressureratio defines the pressure drop.
 14. The method of claim 13, wherein thecontrol law directs the actuator to position the control surface under acondition of low fluid flow, such that a slope of the flow curveapproaches zero at the solution point.
 15. The method of claim 14,wherein the control law directs the actuator to position the controlelement under a condition of choked fluid flow, such that an inverseslope of the flow curve approaches zero at the operating point.
 16. Agas turbine engine comprising: a fan; a compressor section downstream ofthe fan; a combustor section downstream of the compressor section; aturbine section downstream of the combustor section; an actuator,wherein the actuator positions a control surface of an element of thegas turbine engine, the element of the gas turbine engine defining aflow path through an aperture, the aperture defining a pressure dropalong the flow path to regulate fluid flow through the aperture; acontrol law configured to direct the actuator as a function of a modeloutput; a model processor configured to generate the model output, themodel processor comprising: an input object for processing a model inputvector and setting a model operating mode; a set state module forsetting dynamic states of the model processor, the dynamic states inputto an open loop model based on the model operating mode; wherein theopen loop model generates a current state derivatives, solver stateerrors, and synthesized parameters as a function of the dynamic statesand the model input vector, wherein a constraint on the current statederivatives and solver state errors is based on a series of cyclesynthesis modules, each member of the series of cycle synthesis modulesmodeling a component of a cycle of the gas turbine engine and comprisinga series of utilities, the utilities based on mathematical abstractionsof physical laws that govern behavior of the component, the series ofcycle synthesis modules including a flow module for optimized mapping aflow curve relating a compressible flow function to a pressure ratio andfor defining a solution point located on the flow curve and a base pointlocated off the flow curve, wherein the optimized mapping comprisesminimization of curvature of the flow curve related to the pressureratio while minimizing a horizontal portion of the flow curve related tothe compressible flow function; an estimate state module configured todetermine an estimated state of the model based on at least one of aprior state, the current state derivatives, the solver state errors, andthe synthesized parameters; and an output object for processing at leastthe synthesized parameters of the model to determine the model output.17. The gas turbine engine of claim 16, wherein the aperture comprises avariable-area nozzle.
 18. The gas turbine engine of claim 16, whereinthe open loop model generates at least the solver state errors as afunction of a slope solver state defined between the base point and thesolution point.
 19. The gas turbine engine of claim 18, wherein theslope solver state is estimated by moving the solution point along theflow curve, such that the solver state errors are minimized.
 20. The gasturbine engine of claim 19, wherein the control law directs the actuatorto position the control surface based on a feedback that is a functionof the slope solver state, such that the compressible flow functiondefines the fluid flow and the pressure ratio defines the pressure drop.